Finite Group Databasebeta

← C5×#63385 #13083828

Subgroups — C5×#63385 #13083828

Order 1440.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×C9×D8C211yesmaximal, characteristic, complemented
2C5×D72C211yesmaximal, characteristic, complemented
3C5×C9⋊C16C211yesmaximal, characteristic, complemented
4C5×#826—31nomaximal
5C5×D4×C9—21no—
6C5×D36—21no—
7C5×C8×C9C2211yescharacteristic
8#63385C511yesmaximal, characteristic, direct product factor, Hall
9C3×C5×D8D311yescharacteristic
10C5×D24—31no—
11C5×C3⋊C16—31no—
12C22×C5×C9—41no—
13C2×C5×D9—41no—
14C4×C5×C9D411yescharacteristic
15C5×D16—91noHall
16C9×D8C2×C511yescharacteristic, complemented
17D72C2×C511yescharacteristic, complemented
18C9⋊C16C2×C511yescharacteristic, complemented
19C3×C5×D4—21no—
20C5×D12—61no—
21C3×C5×C8C2×D311yescharacteristic
22#826—31no—
23C2×C5×C9—81no—
24C2×C5×C9D811yescharacteristic
25C5×D9—81no—
26C5×D8—91no—
27C5×D8D911yescharacteristic, complemented
28C5×C16—91no—
29D4×C9—21no—
30D36—21no—
31C8×C9C22×C511yescharacteristic
32C22×C3×C5—41no—
33C2×C5×D3—121no—
34C3×C4×C5#6711yescharacteristic
35C3×D8C5×D311yescharacteristic
36D24—31no—
37C3⋊C16—31no—
38C5×C9D1611yescharacteristic, complemented, Hall
39C5×D4—21no—
40C5×D4—181no—
41C5×C8C2×D911yescharacteristic
42C22×C9—41no—
43C2×D9—41no—
44C4×C9C5×D411yescharacteristic
45D16—91noSylow
46C2×C3×C5—81no—
47C2×C3×C5#21311yescharacteristic
48C5×D3—241no—
49C3×D4—21no—
50D12—61no—
51C3×C8C2×C5×D311yescharacteristic
52C22×C5—41no—
53C22×C5—361no—
54C4×C5#61111yescharacteristic
55C2×C9—81no—
56C2×C9C5×D811yescharacteristic
57D9—81no—
58D8—91no—
59D8C5×D911yescharacteristic, complemented
60C16—91no—
61C3×C5#82611yescharacteristic
62C22×C3—41no—
63C2×D3—121no—
64C3×C4C5×#6711yescharacteristic
65C2×C5—81no—
66C2×C5—721no—
67C2×C5#367311yescharacteristic
68C9C5×D1611yescharacteristic, complemented, Sylow
69D4—21no—
70D4—181no—
71C8C2×C5×D911yescharacteristic
72C2×C3—81no—
73C2×C3C5×#21311yescharacteristic
74D3—241no—
75C5#6338511yescharacteristic, direct product factor, Sylow
76C22—41no—
77C22—361no—
78C4C5×#61111yescharacteristic
79C3C5×#82611yescharacteristic
80C2—81no—
81C2—721no—
82C2C5×#367311yescharacteristic
subgroupG/H
centerC2×C5#3673
commutator, cosocleC8×C9C22×C5
FrattiniC3×C8C2×C5×D3
FittingC5×C9×D8C2
socleC2×C3×C5#213
hypercenterC5×D8D9
hypocenterC9C5×D16
LCSG ▷ C8×C9 ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C2×C5 ◁ C4×C5 ◁ C5×C8 ◁ C5×D8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C5×C9×D8C2semidirect
2. C5×D72C2semidirect
3. C5×C9⋊C16C2semidirect
8. #63385C5direct (N × H)
16. C9×D8C2×C5semidirect
17. D72C2×C5semidirect
18. C9⋊C16C2×C5semidirect
27. C5×D8D9semidirect
38. C5×C9D16semidirect
59. D8C5×D9semidirect
68. C9C5×D16semidirect
75. C5#63385direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C5×C9×D82
C5×D722
C5×C9⋊C162
C5×#8263
#633855